Absorbing boundary conditions for the Westervelt equation

The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is pseudo-differential calculus. This approach enables to develop high order boundary conditions in a consistent way which are typically more accurate than their low order analogs. Under the hypothesis of small initial data, we establish local well-posedness for the Westervelt equation with the absorbing boundary conditions. The performed numerical experiments illustrate the efficiency of the proposed boundary conditions for different regimes of wave propagation

The Iteratively Regularized Gau{\ss}-Newton Method with Convex Constraints and Applications in 4Pi-Microscopy

This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to the Newton equations in each iteration step. Convergence of this iterative regularization method is analyzed if both the operator and the right hand side are given with errors and all error levels tend to zero. Our study has been motivated by the joint estimation of object and phase in 4Pi microscopy, which leads to a semi-blind deconvolution problem with nonnegativity constraints. The performance of the proposed algorithm is illustrated both for simulated and for three-dimensional experimental data

Prospects for measuring the gravitational free-fall of antihydrogen with emulsion detectors

The main goal of the AEgIS experiment at CERN is to test the weak equivalence principle for antimatter. AEgIS will measure the free-fall of an antihydrogen beam traversing a moir\'e deflectometer. The goal is to determine the gravitational acceleration g for antihydrogen with an initial relative accuracy of 1% by using an emulsion detector combined with a silicon micro-strip detector to measure the time of flight. Nuclear emulsions can measure the annihilation vertex of antihydrogen atoms with a precision of about 1 - 2 microns r.m.s. We present here results for emulsion detectors operated in vacuum using low energy antiprotons from the CERN antiproton decelerator. We compare with Monte Carlo simulations, and discuss the impact on the AEgIS project.Comment: 20 pages, 16 figures, 3 table

Annihilation of low energy antiprotons in silicon

The goal of the AE$\mathrm{\bar{g}}$IS experiment at the Antiproton Decelerator (AD) at CERN, is to measure directly the Earth's gravitational acceleration on antimatter. To achieve this goal, the AE$\mathrm{\bar{g}}$IS collaboration will produce a pulsed, cold (100 mK) antihydrogen beam with a velocity of a few 100 m/s and measure the magnitude of the vertical deflection of the beam from a straight path. The final position of the falling antihydrogen will be detected by a position sensitive detector. This detector will consist of an active silicon part, where the annihilations take place, followed by an emulsion part. Together, they allow to achieve 1$$ precision on the measurement of $\bar{g}$ with about 600 reconstructed and time tagged annihilations. We present here, to the best of our knowledge, the first direct measurement of antiproton annihilation in a segmented silicon sensor, the first step towards designing a position sensitive silicon detector for the AE$\mathrm{\bar{g}}$IS experiment. We also present a first comparison with Monte Carlo simulations (GEANT4) for antiproton energies below 5 MeVComment: 21 pages in total, 29 figures, 3 table

Building the impedance model of a real machine

A reliable impedance model of a particle accelerator can be built by combining the beam coupling impedances of all the components. This is a necessary step to be able to evaluate the machine performance limitations, identify the main contributors in case an impedance reduction is required, and study the interaction with other mechanisms such as optics nonlinearities, transverse damper, noise, space charge, electron cloud, beam-beam (in a collider). The main phases to create a realistic impedance model, and verify it experimentally, will be reviewed, highlighting the main challenges. Some examples will be presented revealing the levels of precision of machine impedance models that have been achieved

Development of nuclear emulsions operating in vacuum for the AEgIS experiment

For the first time the AEgIS (Antihydrogen Experiment: Gravity, Interferometry, Spectroscopy) experiment will measure the Earth\u2019s local gravitational acceleration g on antimatter through the evaluation of the vertical displacement of an antihydrogen horizontal beam. This will be a model independent test of the Weak Equivalence Principle at the base of the general relativity. The initial goal of a g measurement with a relative uncertainty of 1% will be achieved with less than 1000 detected antihydrogens, provided that their vertical position could be determined with a precision of a few micrometers. An emulsion based detector is very suitable for this purpose featuring an intrinsic sub-micrometric spatial resolution. Nevertheless, the AEgIS experiment re- quires unprecedented operational conditions for this type of detector, namely vacuum environment and very low temperature. An intense R&D activity is presently going on to optimize the detector for the AEgIS experimental requirements with rather encouraging results

A Moiré Deflectometer for Antimatter

The precise measurement of forces is one way to obtain deep insight into the fundamental interactions present in nature. In the context of neutral antimatter, the gravitational interaction is of high interest, potentially revealing new forces that violate the weak equivalence principle. Here we report on a successful extension of a tool from atom optics - the moirè deflectometer - for a measurement of the acceleration of slow antiprotons. The setup consists of two identical transmission gratings and a spatially resolving emulsion detector for antiproton annihilations. Absolute referencing of the observed antimatter pattern with a photon pattern experiencing no deflection allows the direct inference of forces present. The concept is also straightforwardly applicable to antihydrogen measurements as pursued by the AEgIS collaboration. The combination of these very different techniques from high energy and atomic physics opens a very promising route to the direct detection of the gravitational acceleration of neutral antimatter

AEgIS Experiment: Measuring the Acceleration g of the Earth's Gravitational Field on Antihydrogen Beam

The AEgIS experiment [1] aims at directly measuring the gravitational acceleration g on a beam of cold antihydrogen (H) to a precision of 1%, performing the first test with antimatter of the (WEP) Weak Equivalence Principle. The experimental apparatus is sited at the Antiproton Decelerator (AD) at CERN, Geneva, Switzerland. After production by mixing of antiprotons with Rydberg state positronium atoms (Ps), the atoms will be driven to fly horizontally with a velocity of a few 100 ms−1 for a path length of about 1 meter. The small deflection, few tens of μm, will be measured using two material gratings (of period ∼ 80 μm) coupled to a position-sensitive detector working as a moiré deflectometer similarly to what has been done with matter atoms [2]. The shadow pattern produced by the beam will then be detected by reconstructing the annihilation points with a spatial resolution (∼ 2 μm) of each antiatom at the end of the flight path by the sensitive-position detector. During 2012 the experimental apparatus has been commissioned with antiprotons and positrons. Since the AD will not be running during 2013,during the refurbishment of the CERN accelerators, the experiment is currently working with positrons, electrons and protons, in order to prepare the way for the antihydrogen production in late 2014

Measuring the free fall of antihydrogen

After the first production of cold antihydrogen by the ATHENA and ATRAP experiments ten years ago, new second-generation experiments are aimed at measuring the fundamental properties of this anti-atom. The goal of AEGIS (Antimatter Experiment: Gravity, Interferometry, Spectroscopy) is to test the weak equivalence principle by studying the gravitational interaction between matter and antimatter with a pulsed, cold antihydrogen beam. The experiment is currently being assembled at CERN's Antiproton Decelerator. In AEGIS, antihydrogen will be produced by charge exchange of cold antiprotons with positronium excited to a high Rydberg state (n > 20). An antihydrogen beam will be produced by controlled acceleration in an electric-field gradient (Stark acceleration). The deflection of the horizontal beam due to its free fall in the gravitational field of the earth will be measured with a moire deflectometer. Initially, the gravitational acceleration will be determined to a precision of 1%, requiring the detection of about 105 antihydrogen atoms. In this paper, after a general description, the present status of the experiment will be reviewed